Defining polynomial
| $x^{27} + 9 b_{53} x^{26} + 9 b_{52} x^{25} + 9 b_{50} x^{23} + 9 a_{49} x^{22} + 9 b_{48} x^{21} + 3 a_{18} x^{18} + 9 b_{42} x^{15} + 9 a_{39} x^{12} + 9 c_{27} + 27 c_{54} + 3$ |
Invariants
| Residue field characteristic: | $3$ |
| Degree: | $27$ |
| Base field: | $\Q_{3}$ |
| Ramification index $e$: | $27$ |
| Residue field degree $f$: | $1$ |
| Discriminant exponent $c$: | $75$ |
| Artin slopes: | $[2,\frac{17}{6},3]$ |
| Swan slopes: | $[1,\frac{11}{6},2]$ |
| Means: | $\langle\frac{2}{3},\frac{13}{9},\frac{49}{27}\rangle$ |
| Rams: | $(1,\frac{7}{2},5)$ |
| Field count: | $0$ (incomplete) |
| Ambiguity: | $9$ |
| Mass: | $1944$ |
| Absolute Mass: | $1944$ ($0$ currently in the LMFDB) |
Diagrams
The LMFDB does not contain any fields from this family.